Understanding Chi Square Distribution

Last Updated on 13 September 2023

The Chi Square distribution is a fundamental tool in statistical analysis. It is especially crucial in hypothesis testing and in the construction of confidence intervals. The shape of this distribution is entirely determined by a value known as its ‘degrees of freedom.’

Chi Square in Six Sigma

In Six Sigma, we often use the Chi Square distribution in the Analyze phase of the DMAIC cycle. It provides an efficient method to test various kinds of hypotheses, including the independence of two criteria, the goodness of fit, and the variance of normally distributed data.

How to Apply Chi Square in Six Sigma

Applying the Chi Square test in hypothesis testing involves several steps:

1. State Hypothesis: Define a null hypothesis and an alternative hypothesis related to the variables you are studying.
2. Collect Data: Gather enough sample data to test your hypotheses.
3. Calculate Expected Value: Based on your sample size, calculate the expected outcome if the null hypothesis is true.
4. Calculate Chi Square Statistic: Make use of the formula to calculate chi-square statistic
5. Determine P Value: Refer to the Chi Square distribution table to find the P value associated with your calculated statistic.
6. Draw Conclusions: If your P value is less than your predetermined significance level (typically 0.05), you can reject the null hypothesis.